21. 22. 23. 24. Let VE and VAL be1 respectively, prices of European and American options with the same payoff function and expiry time. Using a noarbitrage argument, prove that VE S VA. Consider American put and call with the same strike K ans expiry written on a stock with initial price 8 paying no dividends. Prove that CA PA 2 S K. For the lognormal model with 805) = 8(0) e\"t+\"'/EZ, t > 0, where Z N N0rm(0,1) is a standard normal random variable, nd E[S(t)] and Var(3(t)). You may assume that E[ea+bZ] = ea+b2/2. For the lognormal model with 805) = 8(0) e\"t+"z, t 2 0, where Z N Norm(0,1) is a standard normal random variable, nd E[S'(t)] with some 05 E lR.|